Keywords
- Prime Ideal
- Principal Ideal
- Common Zero
- Diophantine Approximation
- Springer Lecture Note
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
Bertrand, D. and Beukers, F. Equations differentielles et majorations de multiplicités, Ann. Sci. Ecole Norm. Sup. 18 1985, 181–192.
Brownawell, W.D. and Masser, D.W. Multiplicity estimates for analytic functions II, Duke Math J. 47 (1980), 273–295.
Brownawell, W.D. Sequences of Diophantine approximations, J. Number Th. 6(1974), 11–21.
—, Bounds on the degree in the Nullstellensatz, Annals of Math., 126 (1987), 577–591.
—. Borne effective pour l'exposant dans le théorème des zéros, C. R. Acad. Sci. Paris, Sér. I., 305 (1987), 287–290.
—. Aspects of the Hilbert Nullstellensatz, in New Advances in Transcendence, A. Baker, ed, Cambridge University Press, Cambridge, to appear.
—. Local Diophantine Nullstellen inequalities, J. Am. Math. Soc., to appear.
—. Large transcendence degree revisited I. Exponential and CM cases, in Bonn Workshop on Transcendence, G. Wüstholz, ed, Springer Lecture Notes, to appear.
—. Note on a paper of P. Philippon, Mich. Math. J., in press.
Brownawell, W.D. and Tubbs, R. Large transcendence revisited II. The CM case, in Bonn Workshop on Transcendence, G. Wüstholz, ed, Springer Lecture Notes, to appear.
Cassels, J.W.S. An Introduction to Diophantine Approximation, Cambridge University Press, Cambridge, 1957.
Chudnovsky, G.V. Some analytic methods in the theory of transcendental numbers, Inst. of Math., Ukr. SSR Acad. Sci., Preprint IM 74-8 and IM 74-9, Kiev, 1974 = Chapter 1 in Contributions to the Theory of Transcendental Numbers, Am. Math. Soc., Providence, R.I. 1984.
Diaz, G. Grands degrés de transcendance pour des familles d'exponentielles, C. R. Acad. Sci. Paris 305(1987), 159–162.
Gelfond, A.O. Transcendental and Algebraic Numbers, GITTL Moscow 1952 = Dover, New York, 1960.
Jabbouri, E.M. Mesures d'indépendance algébriques sur les groupes algébriques commutatifs, manuscript.
Masser, D.W. and Wüstholz, G. Fields of large transcendence degree generated by values of elliptic functions, Invent. Math. 72 (1983), 407–463.
Nesterenko, Yu.V. On the algebraic dependence of the components of solutions of a system of linear differential equations, Izv. Akad. Nauk SSR Ser. Mat. 38 (1974), 495–512 = Math. UsSR Izv. 8 (1974), 501–518.
—. Estimates for the orders of zeros of functions of a certain class and applications in the theory of transcendental numbers, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), 253–284 = Math. USSR Izv. 11 (1977), 239–270.
—. Bounds for the characteristic function of a prime ideal, Mat. Sbornik 123, No. 1 (1984), 11–34 = Math. USSR Sbornik 51 (1985), 9–32.
—. On algebraic independence of algebraic powers of algebraic numbers, Mat. Sbornik 123, No. 4 (1984), 435–459 = Math. USSR Sbornik 51 (1985), 429–454, brief version in Approximations Diophantiennes et Nombres Transcendants, D. Bertrand and M. Waldschmidt, eds, Birkhäuser Verlag, Verlag, Boston-Basel-Stuttgart, 1983, pp. 199–220.
—. On a measure of the algebraic independence of the values of some functions, Mat. Sbornik 128, No. 4 (1985), 545–568 = Math USSR Sbornik 56 (1986), 545–567.
—. On bounds of measures of algebraically independent numbers, pp. 65–76 in Diophantine Approximations, P.L. Ulnova, ed., Moscow Univ. Press, Moscow, 1985 (Russian).
—. On a measure of algebraic independence of values of the exponential function, Doklady Akad. Nauk SSSR 286, No. 4, 1986, 817–821 = Soviet Math. Doklady 33 (1986), 20–203.
—. On a measure of algebraic independence of values of elliptic functions at algebraic points, Uspehi Mat. Nauk 40 (1985), 221–222 = Russian Math. Surveys 40, No. 4, 1985, 237–238.
—. Measures of algebraic independence of numbers and functions, pp 141–149 in Journées Arithmétiques de Besancon, Asterisque, Vol. 147–148, Soc. Math. France, Paris, 1987.
Osgood, C.F. Nearly perfect systmes and effective generalizations of Shidlovski's theorem, J. Number Th. 13 (1981), 515–540.
Philippon, P. Indépendance algébrique de valeurs des fonctions exponentielles p-adiques, J. reine angew. Math. 329 (1981), 42–51.
—. Pour une théorie de l'indépendance algébrique, Thèse, Université de Paris XI, 1983.
—. Sur les mesures d'indépendance algébrique, pp. 219–233 in Seminaire de Theorie des Nombres, Catherine Goldstein, ed, Birkhäuser, Boston-Basel-Stuttgart, 1985.
—. Critères pour l'indépendance algébrique, Inst. Hautes Etudes Sci. Publ. Math. No. 64, 1986, 5–52.
—. Lemmes de zéros dans les groupes algébriques commutatifs, Bull. Soc. Math. France. 114 (1986), 355=383.
—. Elimination effective, Chap. XXVIII in Journées Algorithmiques-Arithmétiques, Univ. St. Etienne, 1983.
Shidlovsky, A.B. Transcendental Numbers, Nauka, Moscow 1987 (in Russian).
Skoda, H. Applications des techniques L2 à la théorie des idéaux algèbre de fonctions holomorphes avec poids, Ann. Sci. Ecole Norm. Sup. 5 (1972), 545–579.
Tijdeman, R. On the number of zeros of general exponential polynomials, Indag. Math. 33 (1971), 1–7.
Van der Waerden, B.L. Zur algebraischen Geometrie 19, Grundpolynom und zugeordnete Form, Math. Ann. 136(1958), 139–155.
Waldschmidt, M. Algebraic independence of transcendental numbers. Gel'fond's method and its developments, pp. 551–571, in Perspectives in Mathematics, Anniversary of Oberwolfach, W. Jager, J. Moser, R. Remmert, eds, Birkhäuser Verlag, Boston-Basel-Stuttgart, 1984.
—. Algebraic independence of values of exponential and elliptic functions, J. Indian Math. Soc. 48 (1984), 215–228.
—. Groupes algébriques et grands degrés de transcendance, Acta Math. 156 (1986), 253–302.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag
About this paper
Cite this paper
Brownawell, W.D. (1989). Applications of Cayley-Chow forms. In: Schlickewei, H.P., Wirsing, E. (eds) Number Theory. Lecture Notes in Mathematics, vol 1380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086542
Download citation
DOI: https://doi.org/10.1007/BFb0086542
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51397-1
Online ISBN: 978-3-540-46205-7
eBook Packages: Springer Book Archive
